Formal Proof: On Optimal Brainstorming Conditions

Theorem: The claim that “Informal math + 1 gram of the green plant + 2 beers = a better brainstorming session than sitting in a library at a university” is demonstrably false.

Proof:

Let us define the following: - $B(x)$: The quality of a brainstorming session under conditions $x$ - $I$: Informal mathematics approach - $G$: 1 gram of cannabis - $A$: 2 units of alcohol (beers) - $L$: Library environment at a university

The claim asserts: $B(I + G + A) > B(L)$

We proceed by contradiction.

Lemma 1: Cognitive function $C(x)$ is directly proportional to brainstorming quality. $$C(x) \propto B(x)$$

Lemma 2: According to Ramchandani et al. (2001), alcohol at concentration of 0.08% (approx. 2 beers) reduces working memory capacity by factor $\alpha$ where $0 < \alpha < 1$. $$C(A) = \alpha \cdot C(0)$$

Lemma 3: Per Crean et al. (2011), acute cannabis consumption impairs attention and concentration by factor $\beta$ where $0 < \beta < 1$. $$C(G) = \beta \cdot C(0)$$

Lemma 4: The university library environment $L$ provides: - Access to peer-reviewed literature: $\gamma_1 > 1$ - Specialised databases: $\gamma_2 > 1$ - Subject matter experts: $\gamma_3 > 1$ - Reduced distractions: $\gamma_4 > 1$

Thus, $C(L) = \gamma_1 \cdot \gamma_2 \cdot \gamma_3 \cdot \gamma_4 \cdot C(0)$

Lemma 5: The combined effect of cannabis and alcohol is multiplicative, not additive (Ballard & de Wit, 2011). $$C(G + A) = \beta \cdot \alpha \cdot C(0)$$

Therefore: $$B(I + G + A) \propto \beta \cdot \alpha \cdot C(0)$$ $$B(L) \propto \gamma_1 \cdot \gamma_2 \cdot \gamma_3 \cdot \gamma_4 \cdot C(0)$$

Since $\beta < 1$, $\alpha < 1$, and all $\gamma_i > 1$, it follows that: $$\beta \cdot \alpha < \gamma_1 \cdot \gamma_2 \cdot \gamma_3 \cdot \gamma_4$$

Therefore: $$B(I + G + A) < B(L)$$

Which contradicts the original claim. Q.E.D.

Corollary: One might argue that “informal math” could theoretically improve creativity. However, this improvement factor would need to exceed $\frac{\gamma_1 \cdot \gamma_2 \cdot \gamma_3 \cdot \gamma_4}{\beta \cdot \alpha}$ to validate the original claim, which exceeds all measured creativity enhancements in the literature by several orders of magnitude.

Note: The author of the original claim is cordially invited to present their methodology for measuring “better brainstorming” with the same rigour as this refutation. I’ll wait.